Endogenous Recovery and Replication of A Segregated Derivatives Economy with Counterparty Credit, Collateral, and Market Funding

We cast the ongoing debate on FVA onto a segregated derivative economy, where counterparties are defaultable and unable to post collateral fully. The economy exhibits funding asymmetry in that deposit and borrowing have differing rates. A close examination of the micro financing structure of this idealized economy reveals that it is never possible for the economy to buy back its debt to hedge its own default benefit. On the other hand, our analysis shows that the self financing condition substantiates sufficient claim paying resources so that, when a party defaults in the economy, its borrowing and counterparty exposure are paid off in full. Effectively the segregated economy has an endogenous recovery rate of par, and as such there is no self default benefit to hedge. Departing from the existing literature, this paper introduces realistic non-zero haircuts into the self-financing equation when primary risk hedges in stocks or bonds are funded in the repo or securities lending markets. The funding strategy is uniquely defined and the resultant Black-Scholes partial differential equation has additional terms, reflecting different sources of funding and hedging costs, each corresponding to CVA, DVA, and FVA. For non-segregated derivatives economies, an exogenous recovery rate could still apply and consistent CVA/DVA/FVA formula are included with non-zero haircuts fully incorporated